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Manipal MET2012MathematicsQuadratic Equation

If the roots of the equation x^2-2 a x+a^2+a-3=0 are real and less than 3 , then

Options

  1. Aa 2
  2. B2 a 3
  3. C3 a 4
  4. Da 4

Correct answer

A. a 2

Step-by-step solution

Let f(x)=x^2-2 a x+a^2+a-3=0 . Since, f(x) has real roots both less than 3 . Therefore, D 0 and f(3) 0 4 a^2-4 (a^2+a-3 ) 0 and a^2-5 a+6 0 a 3 and a 2 or a 3 a 2

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